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Chords of octacot

Edit 2 2 …
Below are listed the dyadic chords of 11-limit octacot temperament. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by 540/539 are swetismic, by 441/440 werckismic, by 243/242 rastmic, by 245/243 sensamagic, by 245/242 cassacot, and by 100/99 ptolemismic. Those requiring tempering by any two of 540/539, 441/440 or 243/242 are labeled jove, and those requiring both 441/440 and 100/99 octagari. Finally, those requiring any three independent commas of those discussed above are essentially octacot and are labeled octacot.

Octacot has MOS of size 13, 14, 27, 41 and 68. Even 13 notes is enough to supply plenty of harmony, including hexads. It should be noted that the 88 cents temperament is identical to the generator chain of octacot in the 11\150 generator tuning. Hence, if the chains listed under chords are interpreted to belong to the correct octave, the tables below may also be viewed as tables of the chords of 88 cents temperament. The transversals become transversals of 88cET if we leave them unchanged up to 11/6, and raise 9/8, 5/4 and 11/8 to 9/4, 5/2 and 11/4.

Triads

Number
 Chord
 Transversal
 Type
 Hash
1
 0-2-4
 1-10/9-11/9
 otonal
2
 0-2-5
 1-10/9-9/7
 sensamagic
3
 0-3-5
 1-7/6-9/7
 sensamagic
4
 0-2-7
 1-10/9-10/7
 utonal
5
 0-3-7
 1-7/6-10/7
 swetismic
6
 0-4-7
 1-11/9-10/7
 swetismic
7
 0-5-7
 1-9/7-10/7
 otonal
8
 0-3-8
 1-7/6-3/2
 otonal
9
 0-4-8
 1-11/9-3/2
 rastmic
10
 0-5-8
 1-9/7-3/2
 utonal
11
 0-2-9
 1-11/10-11/7
 utonal
12
 0-4-9
 1-11/9-11/7
 utonal
13
 0-5-9
 1-9/7-11/7
 otonal
14
 0-7-9
 1-10/7-11/7
 otonal
15
 0-2-10
 1-10/9-5/3
 utonal
16
 0-3-10
 1-7/6-5/3
 otonal
17
 0-5-10
 1-9/7-5/3
 sensamagic
18
 0-7-10
 1-10/7-5/3
 utonal
19
 0-8-10
 1-3/2-5/3
 otonal
20
 0-2-11
 1-10/9-7/4
 werkismic
21
 0-3-11
 1-7/6-7/4
 utonal
22
 0-4-11
 1-11/9-7/4
 werkismic
23
 0-7-11
 1-10/7-7/4
 werkismic
24
 0-8-11
 1-3/2-7/4
 otonal
25
 0-9-11
 1-11/7-7/4
 werkismic
26
 0-2-12
 1-11/10-11/6
 utonal
27
 0-3-12
 1-7/6-11/6
 otonal
28
 0-4-12
 1-11/9-11/6
 utonal
29
 0-5-12
 1-9/7-11/6
 swetismic
30
 0-7-12
 1-10/7-11/6
 swetismic
31
 0-8-12
 1-3/2-11/6
 otonal
32
 0-9-12
 1-11/7-11/6
 utonal
33
 0-10-12
 1-5/3-11/6
 otonal
34
 0-4-16
 1-11/9-9/8
 rastmic
35
 0-5-16
 1-9/7-9/8
 utonal
36
 0-7-16
 1-10/7-9/8
 werkismic
37
 0-8-16
 1-3/2-9/8
 ambitonal
38
 0-9-16
 1-11/7-9/8
 werkismic
39
 0-11-16
 1-7/4-9/8
 otonal
40
 0-12-16
 1-11/6-9/8
 rastmic
41
 0-2-18
 1-10/9-5/4
 utonal
42
 0-7-18
 1-10/7-5/4
 utonal
43
 0-8-18
 1-3/2-5/4
 otonal
44
 0-9-18
 1-11/7-5/4
 cassacot
45
 0-10-18
 1-5/3-5/4
 utonal
46
 0-11-18
 1-7/4-5/4
 otonal
47
 0-16-18
 1-9/8-5/4
 otonal
48
 0-2-20
 1-11/10-11/8
 utonal
49
 0-4-20
 1-11/9-11/8
 utonal
50
 0-8-20
 1-3/2-11/8
 otonal
51
 0-9-20
 1-11/7-11/8
 utonal
52
 0-10-20
 1-5/3-11/8
 ptolemismic
53
 0-11-20
 1-7/4-11/8
 otonal
54
 0-12-20
 1-11/6-11/8
 utonal
55
 0-16-20
 1-9/8-11/8
 otonal
56
 0-18-20
 1-5/4-11/8
 otonal

Tetrads

Number
 Chord
 Transversal
 Type
 Hash
1
 0-2-4-7
 1-10/9-11/9-10/7
 octarod
2
 0-2-5-7
 1-10/9-9/7-10/7
 sensamagic
3
 0-3-5-7
 1-7/6-9/7-10/7
 octarod
4
 0-3-5-8
 1-7/6-9/7-3/2
 sensamagic
5
 0-2-4-9
 1-11/10-11/9-11/7
 utonal
6
 0-2-5-9
 1-10/9-9/7-11/7
 octarod
7
 0-2-7-9
 1-10/9-10/7-11/7
 ptolemismic
8
 0-4-7-9
 1-11/9-10/7-11/7
 octarod
9
 0-5-7-9
 1-9/7-10/7-11/7
 otonal
10
 0-2-5-10
 1-10/9-9/7-5/3
 sensamagic
11
 0-3-5-10
 1-7/6-9/7-5/3
 sensamagic
12
 0-2-7-10
 1-10/9-10/7-5/3
 utonal
13
 0-3-7-10
 1-7/6-10/7-5/3
 swetismic
14
 0-5-7-10
 1-9/7-10/7-5/3
 sensamagic
15
 0-3-8-10
 1-7/6-3/2-5/3
 otonal
16
 0-5-8-10
 1-9/7-3/2-5/3
 sensamagic
17
 0-2-4-11
 1-10/9-11/9-7/4
 octagari
18
 0-2-7-11
 1-10/9-10/7-7/4
 werkismic
19
 0-3-7-11
 1-7/6-10/7-7/4
 jove
20
 0-4-7-11
 1-11/9-10/7-7/4
 jove
21
 0-3-8-11
 1-7/6-3/2-7/4
 ambitonal
22
 0-4-8-11
 1-11/9-3/2-7/4
 jove
23
 0-2-9-11
 1-10/9-11/7-7/4
 octagari
24
 0-4-9-11
 1-11/9-11/7-7/4
 werkismic
25
 0-7-9-11
 1-10/7-11/7-7/4
 octagari
26
 0-2-4-12
 1-11/10-11/9-11/6
 utonal
27
 0-2-5-12
 1-10/9-9/7-11/6
 octarod
28
 0-3-5-12
 1-7/6-9/7-11/6
 octarod
29
 0-2-7-12
 1-10/9-10/7-11/6
 octarod
30
 0-3-7-12
 1-7/6-10/7-11/6
 swetismic
31
 0-4-7-12
 1-11/9-10/7-11/6
 swetismic
32
 0-5-7-12
 1-9/7-10/7-11/6
 swetismic
33
 0-3-8-12
 1-7/6-3/2-11/6
 otonal
34
 0-4-8-12
 1-11/9-3/2-11/6
 rastmic
35
 0-5-8-12
 1-9/7-3/2-11/6
 swetismic
36
 0-2-9-12
 1-11/10-11/7-11/6
 utonal
37
 0-4-9-12
 1-11/9-11/7-11/6
 utonal
38
 0-5-9-12
 1-9/7-11/7-11/6
 swetismic
39
 0-7-9-12
 1-10/7-11/7-11/6
 octarod
40
 0-2-10-12
 1-10/9-5/3-11/6
 ptolemismic
41
 0-3-10-12
 1-7/6-5/3-11/6
 otonal
42
 0-5-10-12
 1-9/7-5/3-11/6
 octarod
43
 0-7-10-12
 1-10/7-5/3-11/6
 octarod
44
 0-8-10-12
 1-3/2-5/3-11/6
 otonal
45
 0-4-7-16
 1-11/9-10/7-9/8
 jove
46
 0-5-7-16
 1-9/7-10/7-9/8
 werkismic
47
 0-4-8-16
 1-11/9-3/2-9/8
 rastmic
48
 0-5-8-16
 1-9/7-3/2-9/8
 utonal
49
 0-4-9-16
 1-11/9-11/7-9/8
 jove
50
 0-5-9-16
 1-9/7-11/7-9/8
 werkismic
51
 0-7-9-16
 1-10/7-11/7-9/8
 octagari
52
 0-4-11-16
 1-11/9-7/4-9/8
 jove
53
 0-7-11-16
 1-10/7-7/4-9/8
 werkismic
54
 0-8-11-16
 1-3/2-7/4-9/8
 otonal
55
 0-9-11-16
 1-11/7-7/4-9/8
 werkismic
56
 0-4-12-16
 1-11/9-11/6-9/8
 rastmic
57
 0-5-12-16
 1-9/7-11/6-9/8
 jove
58
 0-7-12-16
 1-10/7-11/6-9/8
 jove
59
 0-8-12-16
 1-3/2-11/6-9/8
 rastmic
60
 0-9-12-16
 1-11/7-11/6-9/8
 jove
61
 0-2-7-18
 1-10/9-10/7-5/4
 utonal
62
 0-2-9-18
 1-10/9-11/7-5/4
 octagari
63
 0-7-9-18
 1-10/7-11/7-5/4
 octagari
64
 0-2-10-18
 1-10/9-5/3-5/4
 utonal
65
 0-7-10-18
 1-10/7-5/3-5/4
 utonal
66
 0-8-10-18
 1-3/2-5/3-5/4
 ambitonal
67
 0-2-11-18
 1-10/9-7/4-5/4
 werkismic
68
 0-7-11-18
 1-10/7-7/4-5/4
 werkismic
69
 0-8-11-18
 1-3/2-7/4-5/4
 otonal
70
 0-9-11-18
 1-11/7-7/4-5/4
 octagari
71
 0-7-16-18
 1-10/7-9/8-5/4
 werkismic
72
 0-8-16-18
 1-3/2-9/8-5/4
 otonal
73
 0-9-16-18
 1-11/7-9/8-5/4
 octagari
74
 0-11-16-18
 1-7/4-9/8-5/4
 otonal
75
 0-2-4-20
 1-11/10-11/9-11/8
 utonal
76
 0-4-8-20
 1-11/9-3/2-11/8
 rastmic
77
 0-2-9-20
 1-11/10-11/7-11/8
 utonal
78
 0-4-9-20
 1-11/9-11/7-11/8
 utonal
79
 0-2-10-20
 1-10/9-5/3-11/8
 ptolemismic
80
 0-8-10-20
 1-3/2-5/3-11/8
 ptolemismic
81
 0-2-11-20
 1-10/9-7/4-11/8
 octagari
82
 0-4-11-20
 1-11/9-7/4-11/8
 werkismic
83
 0-8-11-20
 1-3/2-7/4-11/8
 otonal
84
 0-9-11-20
 1-11/7-7/4-11/8
 werkismic
85
 0-2-12-20
 1-11/10-11/6-11/8
 utonal
86
 0-4-12-20
 1-11/9-11/6-11/8
 utonal
87
 0-8-12-20
 1-3/2-11/6-11/8
 ambitonal
88
 0-9-12-20
 1-11/7-11/6-11/8
 utonal
89
 0-10-12-20
 1-5/3-11/6-11/8
 ptolemismic
90
 0-4-16-20
 1-11/9-9/8-11/8
 rastmic
91
 0-8-16-20
 1-3/2-9/8-11/8
 otonal
92
 0-9-16-20
 1-11/7-9/8-11/8
 werkismic
93
 0-11-16-20
 1-7/4-9/8-11/8
 otonal
94
 0-12-16-20
 1-11/6-9/8-11/8
 rastmic
95
 0-2-18-20
 1-10/9-5/4-11/8
 ptolemismic
96
 0-8-18-20
 1-3/2-5/4-11/8
 otonal
97
 0-9-18-20
 1-11/7-5/4-11/8
 octagari
98
 0-10-18-20
 1-5/3-5/4-11/8
 ptolemismic
99
 0-11-18-20
 1-7/4-5/4-11/8
 otonal
100
 0-16-18-20
 1-9/8-5/4-11/8
 otonal

Pentads

Number
 Chord
 Transversal
 Type
 Hash
1
 0-2-4-7-9
 1-10/9-11/9-10/7-11/7
 octarod
2
 0-2-5-7-9
 1-10/9-9/7-10/7-11/7
 octarod
3
 0-2-5-7-10
 1-10/9-9/7-10/7-5/3
 sensamagic
4
 0-3-5-7-10
 1-7/6-9/7-10/7-5/3
 octarod
5
 0-3-5-8-10
 1-7/6-9/7-3/2-5/3
 sensamagic
6
 0-2-4-7-11
 1-10/9-11/9-10/7-7/4
 octacot
7
 0-2-4-9-11
 1-10/9-11/9-11/7-7/4
 octagari
8
 0-2-7-9-11
 1-10/9-10/7-11/7-7/4
 octagari
9
 0-4-7-9-11
 1-11/9-10/7-11/7-7/4
 octacot
10
 0-2-4-7-12
 1-10/9-11/9-10/7-11/6
 octarod
11
 0-2-5-7-12
 1-10/9-9/7-10/7-11/6
 octarod
12
 0-3-5-7-12
 1-7/6-9/7-10/7-11/6
 octarod
13
 0-3-5-8-12
 1-7/6-9/7-3/2-11/6
 octarod
14
 0-2-4-9-12
 1-11/10-11/9-11/7-11/6
 utonal
15
 0-2-5-9-12
 1-10/9-9/7-11/7-11/6
 octarod
16
 0-2-7-9-12
 1-10/9-10/7-11/7-11/6
 octarod
17
 0-4-7-9-12
 1-11/9-10/7-11/7-11/6
 octarod
18
 0-5-7-9-12
 1-9/7-10/7-11/7-11/6
 octarod
19
 0-2-5-10-12
 1-10/9-9/7-5/3-11/6
 octarod
20
 0-3-5-10-12
 1-7/6-9/7-5/3-11/6
 octarod
21
 0-2-7-10-12
 1-10/9-10/7-5/3-11/6
 octarod
22
 0-3-7-10-12
 1-7/6-10/7-5/3-11/6
 octarod
23
 0-5-7-10-12
 1-9/7-10/7-5/3-11/6
 octarod
24
 0-3-8-10-12
 1-7/6-3/2-5/3-11/6
 otonal
25
 0-5-8-10-12
 1-9/7-3/2-5/3-11/6
 octarod
26
 0-4-7-9-16
 1-11/9-10/7-11/7-9/8
 octacot
27
 0-5-7-9-16
 1-9/7-10/7-11/7-9/8
 octagari
28
 0-4-7-11-16
 1-11/9-10/7-7/4-9/8
 jove
29
 0-4-8-11-16
 1-11/9-3/2-7/4-9/8
 jove
30
 0-4-9-11-16
 1-11/9-11/7-7/4-9/8
 jove
31
 0-7-9-11-16
 1-10/7-11/7-7/4-9/8
 octagari
32
 0-4-7-12-16
 1-11/9-10/7-11/6-9/8
 jove
33
 0-5-7-12-16
 1-9/7-10/7-11/6-9/8
 jove
34
 0-4-8-12-16
 1-11/9-3/2-11/6-9/8
 rastmic
35
 0-5-8-12-16
 1-9/7-3/2-11/6-9/8
 jove-
36
 0-4-9-12-16
 1-11/9-11/7-11/6-9/8
 jove
37
 0-5-9-12-16
 1-9/7-11/7-11/6-9/8
 jove
38
 0-7-9-12-16
 1-10/7-11/7-11/6-9/8
 octacot
39
 0-2-7-9-18
 1-10/9-10/7-11/7-5/4
 octagari
40
 0-2-7-10-18
 1-10/9-10/7-5/3-5/4
 utonal
41
 0-2-7-11-18
 1-10/9-10/7-7/4-5/4
 werkismic
42
 0-2-9-11-18
 1-10/9-11/7-7/4-5/4
 octagari
43
 0-7-9-11-18
 1-10/7-11/7-7/4-5/4
 octagari
44
 0-7-9-16-18
 1-10/7-11/7-9/8-5/4
 octagari
45
 0-7-11-16-18
 1-10/7-7/4-9/8-5/4
 werkismic
46
 0-8-11-16-18
 1-3/2-7/4-9/8-5/4
 otonal
47
 0-9-11-16-18
 1-11/7-7/4-9/8-5/4
 octagari
48
 0-2-4-9-20
 1-11/10-11/9-11/7-11/8
 utonal
49
 0-2-4-11-20
 1-10/9-11/9-7/4-11/8
 octagari
50
 0-4-8-11-20
 1-11/9-3/2-7/4-11/8
 jove
51
 0-2-9-11-20
 1-10/9-11/7-7/4-11/8
 octagari
52
 0-4-9-11-20
 1-11/9-11/7-7/4-11/8
 werkismic
53
 0-2-4-12-20
 1-11/10-11/9-11/6-11/8
 utonal
54
 0-4-8-12-20
 1-11/9-3/2-11/6-11/8
 rastmic
55
 0-2-9-12-20
 1-11/10-11/7-11/6-11/8
 utonal
56
 0-4-9-12-20
 1-11/9-11/7-11/6-11/8
 utonal
57
 0-2-10-12-20
 1-10/9-5/3-11/6-11/8
 ptolemismic
58
 0-8-10-12-20
 1-3/2-5/3-11/6-11/8
 ptolemismic
59
 0-4-8-16-20
 1-11/9-3/2-9/8-11/8
 rastmic
60
 0-4-9-16-20
 1-11/9-11/7-9/8-11/8
 jove
61
 0-4-11-16-20
 1-11/9-7/4-9/8-11/8
 jove
62
 0-8-11-16-20
 1-3/2-7/4-9/8-11/8
 otonal
63
 0-9-11-16-20
 1-11/7-7/4-9/8-11/8
 werkismic
64
 0-4-12-16-20
 1-11/9-11/6-9/8-11/8
 rastmic
65
 0-8-12-16-20
 1-3/2-11/6-9/8-11/8
 rastmic
66
 0-9-12-16-20
 1-11/7-11/6-9/8-11/8
 jove
67
 0-2-9-18-20
 1-10/9-11/7-5/4-11/8
 octagari
68
 0-2-10-18-20
 1-10/9-5/3-5/4-11/8
 ptolemismic
69
 0-8-10-18-20
 1-3/2-5/3-5/4-11/8
 ptolemismic
70
 0-2-11-18-20
 1-10/9-7/4-5/4-11/8
 octagari
71
 0-8-11-18-20
 1-3/2-7/4-5/4-11/8
 otonal
72
 0-9-11-18-20
 1-11/7-7/4-5/4-11/8
 octagari
73
 0-8-16-18-20
 1-3/2-9/8-5/4-11/8
 otonal
74
 0-9-16-18-20
 1-11/7-9/8-5/4-11/8
 octagari
75
 0-11-16-18-20
 1-7/4-9/8-5/4-11/8
 otonal

Hexads

Number
 Chord
 Transversal
 Type
 Hash
1
 0-2-4-7-9-11
 1-10/9-11/9-10/7-11/7-7/4
 octacot
2
 0-2-4-7-9-12
 1-10/9-11/9-10/7-11/7-11/6
 octarod
3
 0-2-5-7-9-12
 1-10/9-9/7-10/7-11/7-11/6
 octarod
4
 0-2-5-7-10-12
 1-10/9-9/7-10/7-5/3-11/6
 octarod
5
 0-3-5-7-10-12
 1-7/6-9/7-10/7-5/3-11/6
 octarod
6
 0-3-5-8-10-12
 1-7/6-9/7-3/2-5/3-11/6
 octarod
7
 0-4-7-9-11-16
 1-11/9-10/7-11/7-7/4-9/8
 octacot
8
 0-4-7-9-12-16
 1-11/9-10/7-11/7-11/6-9/8
 octacot
9
 0-5-7-9-12-16
 1-9/7-10/7-11/7-11/6-9/8
 octacot
10
 0-2-7-9-11-18
 1-10/9-10/7-11/7-7/4-5/4
 octagari
11
 0-7-9-11-16-18
 1-10/7-11/7-7/4-9/8-5/4
 octagari
12
 0-2-4-9-11-20
 1-10/9-11/9-11/7-7/4-11/8
 octagari
13
 0-2-4-9-12-20
 1-11/10-11/9-11/7-11/6-11/8
 utonal
14
 0-4-8-11-16-20
 1-11/9-3/2-7/4-9/8-11/8
 jove
15
 0-4-9-11-16-20
 1-11/9-11/7-7/4-9/8-11/8
 jove
16
 0-4-8-12-16-20
 1-11/9-3/2-11/6-9/8-11/8
 rastmic
17
 0-4-9-12-16-20
 1-11/9-11/7-11/6-9/8-11/8
 jove
18
 0-2-9-11-18-20
 1-10/9-11/7-7/4-5/4-11/8
 octagari
19
 0-8-11-16-18-20
 1-3/2-7/4-9/8-5/4-11/8
 otonal
20
 0-9-11-16-18-20
 1-11/7-7/4-9/8-5/4-11/8
 octagari